Chapter_5.lyx

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\begin_layout Section
Conclusion
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Summary
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Here we present a summary of our main original contributions.
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\series bold
Reconstructing voxels.

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 We first proposed a new reconstruction method called Diffusion Nabla Imaging
 (DNI) using an algorithm that directly approximates the Orientation Distributio
n Function using the Laplacian of the signal in q-space.
 Additionally, we found that a family of transforms exists which is a superset
 of DNI.
 We call this the Equatorial Inversion Transform (EIT).
 We showed that EIT has higher angular accuracy in simulations than the
 other methods and that it introduces interesting theoretical foundations
 for the interpretation of the dMRI signal.
 We compared and evaluated different Cartesian-grid q-space dMRI acquisition
 schemes, using methods based on the inverse Fourier transform of the diffusion
 signal, with reconstructions by Diffusion Spectrum Imaging (DSI), Generalized
 Q-sampling Imaging (GQI) and the EIT.
 We also compared EIT against GQI2 which had not been applied to simulated
 or real data until now.
 We found that GQI2 has similar performance with that of the EIT and it
 can generate smooth ODFs.
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Integrating to tracks.

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 Most previously published reconstruction methods are closely linked to
 their own specific tracking method.
 We have formulated a minimal tracking algorithm (EuDX) which is based on
 Euler integration and trilinear interpolation.
 This algorithm integrates voxel level information about fibre orientations
 including multiple crossings, and employs a range of stopping criteria.
 The purpose of this algorithm is to be faithful to the reconstruction results
 rather than try to correct or enhance them by introducing regional or global
 considerations which is the topic of other popular approaches.
 Interestingly, in the experiments with the software phantoms, EuDX performed
 better than a popular probabilistic method.
 With the real data sets it generated more uniform bundles.
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\series bold
Segmenting tracks.
 
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The end goal of clustering is to be able to segment tractography into tracts
 that have biological meaning.
 This is a difficult problem with no well-defined gold standard.
 In order to succeed better, we need to be able to compare the results of
 tractographies, and we need to be able to allow experts in anatomy to interact
 with the results of the tractography.
 Unfortunately, most current methods are so slow to compute that it is not
 practical to compare different methods in reasonable time, and they cannot
 run fast enough for an expert to interact with them in close to real time.
 This thesis provides a complete solution to this problem.
 We developed a surprisingly simple, fully automatic, linear time, clustering
 method (QuickBundles) which reduces massive tractographies into a few easily
 accessible bundles.
 These bundles are characterised by representative tracks which are multi-purpos
e and can be used for interaction with the data or as the basis for applying
 higher complexity clustering methods which would have been impossible or
 too slow with the full data set.
 QuickBundles is as far as we know the fastest existing tractography clustering
 algorithm; providing the opportunity for clinical real-time applications.
 
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Registering tracks.
 
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After applying QuickBundles to tractographies from different subjects, we
 showed how to use the representative tracks to identify robust landmarks
 within each subject which, with similarity metrics which we have introduced,
 we can use them to directly register the different tractographies together
 in a highly efficient way.
 We believe the resulting correspondences provide important evidence for
 the anatomical plausibility of the derived bundles.
 We demonstrated how these methods can be used for group analysis, as well
 as for atlas creation.
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Software
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In providing this thesis we tried to do our best to follow state-of-the-art
 scientific practices.
 One of the important achievements was to create and distribute two different
 software libraries DIPY
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 and FOS
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.
 DIPY is used for dMRI analysis and FOS concentrates only on the visualization
 aspects using OpenGL.
 They are both implemented in the Python programming language.
 We hope that these projects will add up to the stack of existing OpenSource
 projects in the Neuroimaging community like Camino, FSL, DSI Studio and
 SPM.
 We believe that by providing our code open source and not-for-profit we
 allow other researchers to test and extend our findings.
 We believe that this is a factor which can increase the quality of scientific
 research beyond the standard expectations.
 Ioannidis et al.
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 showed that many scientists are avoiding to publish negative results and
 the Neuroimaging community is not an exception.
 We believe that perhaps a way out of this problem is publishing and sharing
 code.
 In that perspective others can confirm, validate and push forward our current
 findings with speeds which were impossible in the past.
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We have enjoyed writing thousands of lines of code in order to generate
 the dMRI algorithms or even the figures of this dissertation.
 Both DIPY and FOS have attracted further developers and scientists from
 acknowledged universities around the world who contribute today to these
 platforms.
 
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Future work
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Here we will describe what our future plans are and the research path we
 wish to take after the completion of this dissertation.
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\series bold
Extending EIT
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.

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Currently the EIT expects Cartesian grid-based q-space data like those used
 in DSI reconstructions.
 However, it seems that because the EIT integrates directional information
 radially on spherical shells it will be straightforward to extend it to
 one or more spherical grid q-space data.
 Spherical grid data are more commonly available and usually they need less
 scanner time.
 In order to make this possible we will need to do further research on spherical
 interpolations.
 Perhaps our spherical smoothing functions described in section 
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 will become handy.
 However, this needs further examination.
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Non-linear Direct Registration
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.

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Our direct registration approach allows only for linear transformations.
 It would be very interesting first to validate our method against volume
 based registration.
 Furthermore, we could investigate a log-Euclidean polyaffine framework
 which allows for smooth non-linear transformations.
 This will be a beautifully challenging problem as the optimization will
 be more difficult.
 Powell's method works perfectly well with the few parameters needed in
 linear registration for this approach.
 However, with the nonlinear difformations many more parameters will need
 fitting.
 Perhaps with the aid of robust optimizers like the Particle Swarm Optimizer
 (PSO) 
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, 
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 we will be able to provide more accurate registration.
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Clinical Applications
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.
 We propose to extend our preliminary involvement with clinical research
 into trichotilomania 
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 from fractional aniso- tropy to track density calculations.
 We would also like to investigate bundle differences with other disorders
 such as autism or schizophrenia.
 Both autism and schizophrenia are considered to have strong relationship
 with defects in white matter architecture caused by disrupted connectivity
 
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.
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Interactive Labeling
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.
 We are developing a scientific visualization tool that solves the problem
 of interacting with tractographies by creating real-time simplifications
 of the underlying anatomical bundle structures.
 The process that we propose works recursively: starting from a small number
 of clusters of streamlines the user decides which clusters to explore.
 Exploring a cluster means that the application re-clusters its content
 at a finer grained level in real-time.
 Of course these representative tracks are provided by QuickBundles which
 can cluster thousands of tracks in milliseconds.
 
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An example of how a medical practitioner can use our visualization software
 to select fibre bundles of their interest.
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Our approach starts by providing a first simplified version (see Fig.
 
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B) of the initial full tractography (see Fig.
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A).
 After visually inspecting the simplified tractography (see Fig.
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B) the practitioner can interactively select one or more representative
 tracks (see Fig.
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C, white track).
 When one or more representative tracks are selected the practitioner can
 see the content of the related clusters (see Fig.
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D).
 In order to explore the detailed structure of the selection the user may
 ask to re-cluster the selected BOIs into smaller clusters (see Fig.
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E).
 In that way one can further refine his previous selection.
 After selecting one or more of the small clusters through their representatives
 (see Fig.
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F, white tracks) the user can repeat the visual inspection step (Fig.
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G), and the re-clustering step (Fig.
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H) as required in order to unveil the local structures (Fig.
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I) which are interesting to their work.
 
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Direct track correspondence between different subjects.
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Shape Correspondence
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Using multi-brain visualization we were able to have a first investigation
 of shape correspondence
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 of tracks between different subjects (see Fig.
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).
 We would like to augment this first implementation from track to bundle
 correspondence.
 In other words a medical practitioner could select a representative track
 or a bundle in one subject and see in real-time the corresponding bundles
 in the other subjects.
 We imagine this as an amalgamation of the tools presented in Fig.
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 and 
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 which are developed in DIPY and FOS.
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Microstructure
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 Our work up till now has focused on estimating the structure of white matter
 in the brain from standard diffusion MRI acquisitions.
 However, these acquisitions provide voxel sizes of about 
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mm.
 Axon fibres, which are about one micron in diameter, are much smaller than
 single voxels.
 Nevertheless, diffusion MRI can provide information on the distribution
 of microstructural features, such as the fibre orientation, fibre diameter
 or density, within each voxel.
 We would also like to extend our work in that area of microanatomy tracking
 which has recently shown very interesting results 
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.
 This high resolution domain require model-fitting of many parameters.
 It would be interesting to investigate if EIT or other non-parametric ideas
 could help alleviate this problem.
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Every participant received a picture of his tractography as a gift for their
 help to our experiments.
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New frontiers
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White matter fibre crossings 
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--
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 from the voxel level to the tractography and bundle level 
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--
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 have been a major motivation for this thesis.
 In March 
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, Wedeen et al.
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 published in Science Magazine a fascinating work that reinforces the importance
 of these topics.
 They showed that they can identify in the tractographies of the brains
 of humans and other animals (in vivo and in vitro) fibre bundles which
 are in agreement with confocal microscopy and other staining techniques.
 The authors clarified that a grid-like structure is prevalent in the brain
 i.e.
 fibre bundles crossing in more areas than would previously have been expected.
 Furthermore, they also showed that the bundles curve more vigorously than
 previously understood.
 We believe that in this thesis we have significantly enhanced and extended
 the techniques that were used to establish these ground-breaking results,
 and have created a framework for them to be applied by the neuroscience
 community.
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In bringing this thesis to a close we would like to thank the participants
 who took part in our imaging studies.
 To honour them we created special pictures of their tractographies like
 the one shown in Fig.
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 which were subsequently presented to them.
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We are very glad to see that the pictures we generate are both beautiful
 and useful pushing our knowledge and inspiration for the advancement of
 brain mapping.
 To honour our participants who took part in our experiments we gave them
 a picture of their tractography like the one shown in Fig.
 
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.
 Albert Einstein suggested that imagination is even more important than
 knowledge.
 Perhaps one day of our near future we will be able to reconstruct single
 axons in vivo and in great precision.
 I hope I will be around to see it happening and help accomplish this achievemen
t.
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